Linear Algebra - Vector space stuff I can't do

Hey,

I've been given 2 questions to do, I think I've got the first one but I have no idea where to start with the second:

1.

Are the solutions to y'' -y' + y =1 a vector space over the real numbers?

I think not. The solutions you're gonna get are of the form y=Kexp(stuff) + Wexp(stuff) +1, this then means that A(solution1) + B(solution2) won't form another solution because of the +1 at the end. (With solution 1 and 2 just being random solutions, and A and B real numbers).

2.

Work out the dimensions of U, V, UnV, U+V, where U,V are subspaces of R^3:

U=SPAN[ (1, -1, 0, 0) , (1, 1, 0, 0) , (1, 1, 0, 1)]

V=SPAN[ (0,1,0,-1) , ( 0, 1, 1, 0) , (0,0,1,1) ]

But if you imagine those as vectors going downwards (I don't know how to use latex)

Thanks a lot if anyone can help me :smile:

Reply 1

SimonM

1. You are correct, but you'd do better to show it by contradicting on of the vector space axioms. Namely, is it closed under addition?

2. What have you done of the second question so far?

Reply 2

jobo3

SimonM

1. You are correct, but you'd do better to show it by contradicting on of the vector space axioms. Namely, is it closed under addition?

2. What have you done of the second question so far?